MAA Press: An Imprint of the American Mathematical Society
The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian.
The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.
Undergraduate and graduate students and researchers interested in the history of mathematics.
AMS/MAA Textbooks Volume: 61; 2020; 724 pp; Softcover
MSC: Primary 01;
Print ISBN: 978-1-4704-4382-5
This latest revision of this successful textbook provides a comprehensive introduction to probability and random processes
Suitable and accessible for mathematics undergraduates and postgraduates, regardless of background
Moves from basic mathematical ideas to advanced topics including Markov processes, martingales and diffusions
New to this Edition:
300 new exercises and problems, with over 1300 in total
New sections on coupling from the past, Levy processes, self-similarity and stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains
Hardback
ISBN: 9780198847601
Paperback
ISBN: 9780198847595
Published: 16 July 2020
688 Pages
246x171mm
Provides a complete proof of desingularization of surfaces, and several other
well-known results not previously published in the literature
Briefly summarizes the history of the topic, with numerous readable
references
Written in an accessible style, ideal for non-specialists
Features numerous useful computations, serving as a source of inspiration for
experts exploring bigger dimensions
This book provides a rigorous and self-contained review of desingularization theory. Focusing
on arbitrary dimensional schemes, it discusses the important concepts in full generality,
complete with proofs, and includes an introduction to the basis of Hironakafs Theory. The core
of the book is a complete proof of desingularization of surfaces; despite being well-known, this
result was no more than folklore for many years, with no existing references. Throughout the
book there are numerous computations on standard bases, blowing ups and characteristic
polyhedra, which will be a source of inspiration for experts exploring bigger dimensions.
Beginners will also benefit from a section which presents some easily overlooked pathologies.
Mathematics : Algebra
1st ed. 2020, VIII, 258 p. 41 illus.
Softcover
ISBN 978-3-030-52639-9
Product category : Proceedings
Series : Lecture Notes in Mathematics
From Quadratic Equations to Quadratic Reciprocity
Introduces foundational concepts in number theory, set theory, and algebra
in an accessible and motivated way
Includes over 300 carefully structured exercises to aid understanding
Helps the reader develop basic programming skills for mathematical
computations
This book takes the reader on a journey from familiar high school mathematics to
undergraduate algebra and number theory. The journey starts with the basic idea that new
number systems arise from solving different equations, leading to (abstract) algebra. Along this
journey, the reader will be exposed to important ideas of mathematics, and will learn a little
about how mathematics is really done. Starting at an elementary level, the book gradually
eases the reader into the complexities of higher mathematics; in particular, the formal
structure of mathematical writing (definitions, theorems and proofs) is introduced in simple
terms. The book covers a range of topics, from the very foundations (numbers, set theory) to
basic abstract algebra (groups, rings, fields), driven throughout by the need to understand
concrete equations and problems, such as determining which numbers are sums of squares.
Some topics usually reserved for a more advanced audience, such as Eisenstein integers or
quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the
reader to open source software for computations, to enhance understanding of the material
and nurture basic programming skills. For the more adventurous, a number of Outlooks
included in the text offer a glimpse of possible mathematical excursions. This book supports
readers in transition from high school to university mathematics, and will also benefit university
students keen to explore the beginnings of algebraic number theory. It can be read either on
its own or as a supporting text for first courses in algebra or number theory, and can also be
used for a topics course on Diophantine equations
Mathematics : Number Theory
Due 2020-12-08
1st ed. 2020, XIX, 344 p.
Softcover
ISBN 978-3-030-55232-9
Product category : Undergraduate textbook
Series : SUMS Readings
Provides an overview of the most important special functions of Fractional
Calculus including new results
Presents a complete and self-contained description of all aspects of the
theory and application of the Mittag-Leffler functions
The introduced functions are of great importance for soving differential and
integral equations of fractional order
The 2nd edition of this book is essentially an extended version of the 1st and provides a very
sound overview of the most important special functions of Fractional Calculus. It has been
updated with material from manyrecentpapers and includes several surveys of important
results known before the publication of the 1st edition, but not covered there. As a result of
researchersf and scientistsf increasing interest in pure as well as applied mathematics in nonconventional models,
particularly those using fractional calculus, Mittag-Leffler functions have
caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler
functions, this volume offers a self-contained, comprehensive treatment, ranging from rather
elementary matters to the latest research results. In addition to the theory the authors devote
some sections of the work to applications, treating various situations and processes in
viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics.
In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes
that progress or decay too slowly to be represented by classical functions like the exponential
function andrelated special functions. The book is intended for a broad audience, comprising
graduate students, university instructors and scientists in the field of pure and applied
mathematics, as well as researchers in applied sciences like mathematical physics, theoretical
chemistry, bio-mathematics, control theory and several other related areas
Mathematics : Mathematical Physics
Due 2020-11-28
2nd ed. 2020, XVI, 536 p.
19 illus., 11 illus. in color.
Hardcover
ISBN 978-3-662-61549-2
Product category : Monograph
Series : Springer Monographs in Mathematics
Discusses the fundamental topics in the theory of complex algebraic surfaces
Serves as an introductory textbook for graduate students of algebraic geometry
Requires only a basic knowledge of complex manifolds as a prerequisite
This is an English translation of the book in Japanese, published as the volume 20 in the
series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by
Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the
theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for
curves on a surface and Noether's formula for the arithmetic genus. It also discusses the
behavior of the pluri-canonical maps of surfaces of general type as a practical application of
the general theory. The book is aimed at graduate students and also at anyone interested in
algebraic surfaces, and readers are expected to have only a basic knowledge of complex
manifolds as a prerequisite.
Mathematics : Algebraic Geometry
1st ed. 2020, XIII, 75 p. 45 illus.
Softcover
ISBN 978-981-15-7379-8
Product category : Brief
Series : SpringerBriefs in Mathematics
Ring and Module-theoretic Properties, Matrix and Grobner Methods, and Applications
Covers in a single text theoretical aspects of non-commutative rings and
algebras of polynomial type, matrix and algorithmic Grobner methods, and
applications to non-commutative algebraic geometry
Includes a huge number of examples illustrating the theoretical results and
algorithms
Provides a unified treatment of quantum algebras, which arise in
mathematical physics
This monograph is devoted to a new class of non-commutative rings, skew Poincare?Birkhoff?
Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic
/homological properties, it goes on to investigate finitely generated projective modules over
skew PBW extensions from a matrix point of view. To make this theory constructive, the theory
of Grobner bases of left (right) ideals and modules for bijective skew PBW extensions is
developed. For example, syzygies and the Ext and Tor modules over these rings are computed.
Finally, applications to some key topics in the noncommutative algebraic geometry of quantum
algebras are given, including an investigation of semi-graded Koszul algebras and semi-graded
Artin?Schelter regular algebras, and the noncommutative Zariski cancellation problem. The
book is addressed to researchers in noncommutative algebra and algebraic geometry as well
as to graduate students and advanced undergraduate students.
Mathematics : Associative Rings and Algebras
Due 2020-11-28
1st ed. 2020, X, 574 p.
Hardcover
ISBN 978-3-030-53377-9
Product category : Monograph
Series : Algebra and Applications